Strong completeness for a class of stochastic differential equations with irregular coefficients

We prove the strong completeness for a class of non-degenerate SDEs, whose coefficients are not necessarily uniformly elliptic nor locally Lipschitz continuous nor bounded. Moreover, for each $t$, the solution flow $F_t$ is weakly differentiable and for each $p>0$ there is a positive number $T(p)$ such that for all $t<T(p)$, the solution flow $F_t(\cdot)$ belongs to the Sobolev space W_{\loc}^{1,p}. The main tool for this is the approximation of the associated derivative flow equations. As an application a differential formula is also obtained

Dyson-Schwinger Equations with a Parameterized Metric

We construct and solve the Dyson-Schwinger equation (DSE) of quark propagator with a parameterized metric, which connects the Euclidean metric with the Minkowskian one. We show, in some models, the Minkowskian vacuum is different from the Euclidean vacuum. The usual analytic continuation of Green function does not make sense in these cases. While with the algorithm we proposed and the quark-gluon vertex ansatz which preserves the Ward-Takahashi identity, the vacuum keeps being unchanged in the evolution of the metric. In this case, analytic continuation becomes meaningful and can be fully carried out.Comment: 10 pages, 7 figures. To appear in Physical Review

Effects of tidally enhanced stellar wind on the horizontal branch morphology of globular clusters

Metallicity is the first parameter to influence the horizontal branch (HB) morphology of globular clusters (GCs). It has been found, however, that some other parameters may also play an important role in affecting the morphology. While the nature of these important parameters remains unclear, they are believed to be likely correlated with wind mass-loss of red giants, since this mass loss determines their subsequent locations on the HB. Unfortunately, the mass loss during the red giant stages of the stellar evolution is poorly understood at present. The stellar winds of red giants may be tidally enhanced by companion stars if they are in binary systems. We investigate evolutionary consequences of red giants in binaries by including tidally enhanced stellar winds, and examine the effects on the HB morphology of GCs. We find that red, blue, and extreme horizontal branch stars are all produced under the effects of tidally enhanced stellar wind without any additional assumptions on the mass-loss dispersion. Furthermore, the horizontal branch morphology is found to be insensitive to the tidal enhancement parameter, Bw. We compare our theoretical results with the observed horizontal branch morphology of globular cluster NGC 2808, and find that the basic morphology of the horizontal branch can be well reproduced. The number of blue horizontal branch stars in our calculations, however, is lower than that of NGC 2808.Comment: 7 pages, 4 figures, 2 tables, accepted for publication in Astronomy & Astrophysic

Phase diagram and critical endpoint for strongly-interacting quarks

We introduce a method based on the chiral susceptibility, which enables one to draw a phase diagram in the chemical-potential/temperature plane for strongly-interacting quarks whose interactions are described by any reasonable gap equation, even if the diagrammatic content of the quark-gluon vertex is unknown. We locate a critical endpoint (CEP) at (\mu^E,T^E) ~ (1.0,0.9)T_c, where T_c is the critical temperature for chiral symmetry restoration at \mu=0; and find that a domain of phase coexistence opens at the CEP whose area increases as a confinement length-scale grows.Comment: 4 pages, 3 figure

Classification of multipartite entanglement containing infinitely many kinds of states

We give a further investigation of the range criterion and Low-to-High Rank Generating Mode (LHRGM) introduced in \cite{Chen}, which can be used for the classification of $2\times{M}\times{N}$ states under reversible local filtering operations. By using of these techniques, we entirely classify the family of $2\times4\times4$ states, which actually contains infinitely many kinds of states. The classifications of true entanglement of $2\times(M+3)\times(2M+3)$ and $2\times(M+4)\times(2M+4)$ systems are briefly listed respectively.Comment: 11 pages, revte

Phase diagram and thermal properties of strong-interaction matter

We introduce a novel procedure for computing the (mu,T)-dependent pressure in continuum QCD; and therefrom obtain a complex phase diagram and predictions for thermal properties of the system, providing the in-medium behaviour of the trace anomaly, speed of sound, latent heat and heat capacity.Comment: 6 pages, 4 figures. Minor amendments in the version accepted for publicatio